Both Least Squares Methods Make Specific Assumptions About Errors Which Affect Bias

  The apparent bias in the ordinary least squares fit appears to be due to a subtle error in the assumption concerning the errors in the x-axis. Ordinary least squares assumed the values of the x-axis were exact while transverse least squares assumes both variables are subject to error. If one removes the errors in the x values one finds ordinary least squares gives the better estimate for the averages of the coefficients of the line when the law of large numbers is applied to the cumulative averages.

A discrepancy between the assumptions in the fit method and the data can result in a blunder which is an example of a systematic error.